Sentence examples for matrix up to from inspiring English sources

A frame is determined by its Gram matrix up to unitary equivalence.

Since P is weakly representable, the transformed diagonal sequence is still a row of the matrix, up to provable equivalence.

The Eocene reservoirs are mainly sandstone with inferred clay matrix up to 20% and some calcareous cementation.

It implies that mesoporous material enhances the mechanical properties of the matrix up to a great extent.

Ultimate tensile strength was elevated from 0.08±0.04 MPa in matrix up to 1.21±0.29 for fiber fraction of 30%.

We give the interaction matrix up to an exponentially small error, measured by Agmon's distance between the wells.

Addition of ceramic particles was found to reinforce both matrices up to a critical concentration (< 3 w/v%).

The biosynthetic phenotype of native cells isolated from NPs was preserved in alginate matrices up to 4 weeks of culturing.

As a required demand, the code also include symplectic integration methods (based on a correcting procedure for aberration matrices) up to an approximation order.

VEGF encapsulation consistently improved angiogenesis in vivo with both type of 3D matrices: up to 7.5- to 3.5-times more endothelial and red blood cells were observed, respectively, into hydrogels and scaffolds.

By making use of a new formulation of the EBCM integrals specifically designed to avoid numerical cancellations, we are able to obtain accurate matrices up to high multipole order, and study the effect of changing this order on both the individual matrix elements and derived physical observables.